Potential estimates for quasi-linear parabolic equations

TL;DR

This paper derives pointwise estimates for solutions to a class of quasi-linear degenerate parabolic equations with Radon measure data, using nonlinear Wolff potentials to extend understanding of solution behavior.

Contribution

It introduces a novel method to estimate solutions of divergence type quasi-linear parabolic equations with measure data using nonlinear Wolff potentials.

Findings

Established pointwise bounds for solutions

Extended potential theory to degenerate parabolic equations

Provided tools for analyzing measure data in PDEs

Abstract

For a class of divergence type quasi-linear degenerate parabolic equations with a Radon measure on the right hand side we derive pointwise estimates for solutions via nonlinear Wolff potentials.